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Warm-Up What does the motion of gas molecules look like? Why does a balloon inflate when you blow it up? Why will soda explode from a bottle if opened after shaking it? – PowerPoint PPT presentation

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Title: Warm-Up


1
Warm-Up
  • What does the motion of gas molecules look like?
  • Why does a balloon inflate when you blow it up?
    Why will soda explode from a bottle if opened
    after shaking it?

2
Chapter 5
  • The Gas Laws

3
Section 5.1- Pressure
  • Force per unit area (P force/area).
  • Gas molecules fill container.
  • Molecules move around and hit sides.
  • Collisions are the force.
  • Container is the area.
  • Measured with a barometer.

4
How Does A Barometer Work?
Vacuum
760 mm Hg
  • The pressure of the atmosphere at sea level will
    cause the column of mercury to rise to 760 mm Hg.
  • 1 atm 760 mm Hg

Pressure of atmosphere pushes on Hg
As a result, Hg rises up into the glass tube
Hg stops rising when its equal to atmospheric
pressure
5
Units of pressure
  • 1 atmosphere 760 mm Hg
  • 1 mm Hg 1 torr
  • 1 atm 101,325 Pascals 101.325 kPa
  • The first two are provided on the AP equation
    sheet. No need to memorize the third- I assume
    youll be given that if you need to use it.

6
THE GAS LAWS OF BOYLE, CHARLES, AND AVOGADRO
  • Section 5.2

7
About the Laws
  • You should be aware of the following laws,
    however we will not focus heavily on them as they
    can be derived from the ideal gas law.
  • After briefly going through each of the following
    laws, we will see how to derive each from the
    ideal gas law.

8
Boyles Law
  • Pressure and volume are inversely related at
    constant temperature.
  • P1V1 P2V2
  • As one goes up, the other goes down.
  • Ex if P increases (at constant T), V must go
    down
  • Further studies show that Boyles Law is only
    true at very low P
  • This will be discussed more in 5.8
  • Gases that obey these laws are called ideal
    gases.

9
Charless Law
  • Volume of a gas varies directly with the
    temperature at constant pressure.
  • V1 V2
  • T1 T2
  • As one goes up/down, so does the other.


10
Avogadro's Law
  • At constant temperature and pressure, the volume
    of gas is directly related to the number of
    moles.
  • V1 V2
  • n1 n2
  • As one goes up/down, so does the other.


11
Gay- Lussac Law
  • At constant volume, pressure and temperature are
    directly related.
  • P1 P2
  • T1 T2
  • As one goes up/down, so does the other.


12
Combined Gas Law
  • Combination of Boyles Law, Charles Law, and
    Gay-Lussac Law.
  • Moles of gas remain constant.
  • P1V1 P2V2
  • T1 T2


13
Summary
  • Boyles P1V1 P2V2
  • Charles V1/T1 V2/T2
  • Avogadros V1/n1 V2/n2
  • Gay-Lussac P1/T1 P2/T2
  • Combined P1V1/T1 P2V2/T2
  • Thats a lot of laws! Or we can just use the
    Ideal Gas Law!

14
Combined Gas Law Cont.
  • Ex A 2.3L sample of gas has a pressure of 1.2atm
    at 200.K. If the pressure is raised to 1.4atm and
    the temperature is increased to 300.K, what is
    the volume of the gas?
  • V2 P1V1T2
  • T1P2
  • V2 3.0 L

15
Practice
  • Ex A 12.2L sample of gas has 0.50mol of O2 at
    1atm and 25C. How many moles of O2 would occupy
    19.4L at the same temperature and pressure?
  • Solution V1/n1 V2/n2
  • (12.2L)/(0.50mol) (19.4L)/(n2)
  • n2 0.80mol
  • In other words, 0.80mol of O2 would be required
    to fill 19.4L in order to keep the same pressure
    as 0.50mol of O2 in 12.2L.

16
AP Practice Question
  • A sample of argon gas is sealed in a container.
    The volume of the container is doubled. If the
    pressure remains constant, what must happen to
    the temperature?
  • It doesnt change.
  • It is halved.
  • It is doubled.
  • It is squared.

17
Demonstration Warm-Up!
  • Observe the demonstration.
  • Keep in mind the properties of gases we have
    discussed so far P, V, T, and n.
  • Think about these properties before and after
    imploding the can. Why do you think the can was
    crushed?
  • As temperature decreases, so does the pressure
    and volume.
  • Remind you of a law we looked at?

18
Sections 12 Homework
  • Pgs. 217-218 2, 6, 34, 35

19
THE IDEAL GAS LAW
  • Section 5.3

20
Ideal Gas Law
  • PV nRT
  • At standard temperature and pressure (STP) V
    22.4L at 1atm, 0ºC, and n 1mol. These
    conditions were used to determine R (ideal gas
    constant)
  • R 0.08206 L atm/mol K
  • 8.314 J/mol K
  • 62.36 L torr/mol K
  • Tells you about a gas NOW.
  • The other laws tell you about a gas when it
    changes.

KNOW THIS!
Choose R value according to units of P
21
Ideal Gas Law Cont.
  • Looking back at the possible values for R, you
    will notice that all units for temperature are in
    K.
  • When using the ideal gas law for calculations,
    convert all temperatures to K!
  • Recall conversion K C 273 (provided on AP
    equation sheet)

22
Ideal Gas Law Derivation Practice
  • May be asked to prove one of the laws discussed
    before!
  • Strategy get all constants in the ideal gas law
    on one side and changing variables on the other.
  • We will go several of these in class.

23
AP Practice Question
  • A 1.15mol sample of carbon monoxide gas has a
    temperature of 27C and a pressure of 0.300atm.
    If the temperature is lowered to 17C at constant
    volume, what is the new pressure?
  • a) 0.290atm c) 0.206atm
  • b) 0.519atm d) 0.338atm

24
Ideal Gas Law- Why Ideal?
  • Ideal gases are hypothetical substances.
  • Gases only approach ideal behavior at low
    pressure (lt 1 atm) and high temperature.
  • They do not behave exactly according to this law,
    but they behave closely enough.
  • Law provides good estimates of gas behavior under
    these conditions.
  • Unless told otherwise, assume ideal gas behavior
    and use the ideal gas law.

25
AP Practice Question
  • A sample of aluminum metal is added to HCl. How
    many grams of aluminum metal must be added to an
    excess of HCl to produce 33.6L of hydrogen gas at
    STP?
  • 18.0g
  • 35.0g
  • 27.0g
  • 4.50g

26
Section 3 Homework
  • Complete the gas laws worksheet AND 33, 40, 43,
    52 on pg. 219-221.

27
GAS STOICHIOMETRY
  • Section 5.4

28
Gases and Stoichiometry
  • Reactions involve moles of substances.
  • Recall that at STP (0ºC and 1 atm) 1mol of any
    gas occupies 22.4 L.
  • At STP this can be a conversion factor
    1mol/22.4L or 22.4L/1mol
  • If not at STP, use the ideal gas law to calculate
    moles or volume of a substance.

29
Section 4 Example
  • Quicklime (CaO) is produced by the thermal
    decomposition of calcium carbonate. Calculate the
    volume of carbon dioxide produced at STP if 152g
    of calcium carbonate are completely decomposed.
  • CaCO3 ? CaO CO2
  • Convert to moles 152g x 1mol 1.52mol

  • 100.09g CaCO3
  • 11 mole ratio of CaCO3 to CO2 1.52mol CO2
  • Use STP conditions stoichiometry
  • At STP 1mol 22.4L
  • 1.52mol x (22.4L/1mol) 34.1L CO2

Can double check using ideal gas law
30
Gas Density and Molar Mass
  • Recall D m/V
  • Let mmolar stand for molar mass
  • mmolar m/n so n m/mmolar
  • PV nRT solve for n n PV/RT
  • Thus m/mmolar PV/RT
  • Solve for mmolar mmolar mRT/VP
  • Replace m/V with D mmolar DRT/P
  • If density, temperature, and pressure are known,
    molar mass can be found.

31
AP Practice Question
  • Determine the formula for a gaseous silane
    (SinH2n2) if its density is 5.47g/L at 0ºC and
    1.00atm.
  • There are several ways to solve!
  • SiH4
  • Si2H6
  • Si3H8
  • Si4H10

32
Section 4 Homework
  • Pg. 220-221 51, 54, 57, 63, 64

33
DALTONS LAW OF PARTIAL PRESSURES
  • Section 5.5

34
Daltons Law of Partial Pressures
  • The total pressure in a container is the sum of
    the pressure each gas would exert if it were
    alone in the container.
  • Total pressure sum of partial pressures.
  • Ptot P1 P2 P3 ...
  • P1, P2, P3 are individual gases
  • From the ideal gas law PTotal (nTotal)RT

V
35
Partial Pressures Cont.
  • What does Daltons Law tell us about ideal gases?
  • Total of gas particles, not their identities,
    is important.
  • V of individual gas particles doesnt affect the
    total P.
  • Forces between gas particles doesnt affect the
    total P.
  • If these were important, the different identities
    of gas particles would affect the total P
    differently.

36
AP Practice Question
  • A gaseous mixture at 25C contained 1mol CH4 and
    2mol O2, and P 2atm. The gases underwent the
    following reaction
  • CH4(g) 2O2(g) ? CO2(g) 2H2O(g)
  • What is the P in the container after the reaction
    goes to completion and the T is allowed to return
    to 25C?
  • 1atm
  • 2atm
  • 3atm
  • 4atm

37
AP Practice Question
  • A sealed, rigid container is filled with three
    identical gases A, B, and C. The partial
    pressure of each gas is known as well as T and V.
    What additional information is needed to find the
    masses of the gases in the container?
  • a) average distance travelled between molecular
    collisions
  • b) the intermolecular forces
  • c) the molar masses of the gases
  • d) the total pressure

38
The mole fraction
  • Ratio of moles of a substance to the total moles.
  • symbol is Greek letter chi c
  • c1 n1 P1
  • ntot Ptot
  • Mole fractions have no units!

39
AP Practice Question
  • A reaction makes a mixture of CO2, CO, and H2O.
    The gaseous products contained 0.60mol CO2,
    0.30mol CO, and 0.10mol H2O. If the total P is
    0.80atm, what is the partial P of CO?
  • 0.24atm
  • 0.34atm
  • 0.080atm
  • 0.13atm

40
Vapor Pressure
  • Water evaporates!
  • When water evaporates, the resulting water vapor
    has a pressure.
  • Vapor pressure changes with T- must be looked up.
  • Gases are often collected over water so the vapor
    pressure of water must be subtracted from the
    total pressure.
  • Vapor pressure must be given.

41
AP Practice Question
  • A sample of methane gas was collected over water
    at 35C. The sample had a total pressure of 756mm
    Hg. Determine the partial pressure of methane gas
    in the sample. (Vapor pressure of water at 35C
    is 41mm Hg.)
  • 760mm Hg
  • 41mm Hg
  • 715mm Hg
  • 797mm Hg

42
Section 5 Homework
  • Pg. 221-222 65, 67, 69, 72

43
Collapsing Can Demo
  • Watch the demonstration.
  • Why did the can collapse?
  • -The heat vaporized the water, which in turn
    increased P and pushed air out of the can.
  • -When the can was inverted the water vapor
    quickly cooled. This caused a quick drop in P
    (created a partial vacuum because essentially no
    air was left to maintain P).
  • -The atmospheric P outside of the can was much
    greater than P inside of the can, which allowed
    the can to be crushed.

44
THE KINETIC MOLECULAR THEORY OF GASES
  • Section 5.6

45
Kinetic Molecular Theory (KMT)- Explains Behavior
Properties of Gases
  • Gases are made up of molecules or atoms.
  • V of particles can be ignored (very small in
    comparison to distance b/t particles).
  • Particles constantly move and collide with each
    other and the walls of the container. Collisions
    with the walls of the container cause P of the
    gas.
  • Particles dont attract or repel each other when
    they collide, its elastic (no KE is lost- its
    transferred).
  • The average KE is proportional to the Kelvin T.

46
KMT Cont.
  • Assumes gases are ideal.
  • BUT no gases are truly ideal- they only approach
    ideal behavior (specifically nonpolar gases at
    low P and high T).
  • In reality, gases DO have V (although small), and
    they CAN interact with each other.
  • Even so, assuming ideal behavior gives us good
    enough answers about properties of gases.

47
KMT
  • 3 describes motion lets quantify it
  • urms v(3RT/mmolar)
  • urms is root mean square velocity
  • R value used is 8.314J/molK
  • molar mass in kg/mol (b/c J kgm2/s2)
  • 5 KE per mole (average KE) 3/2 RT
  • Recall definition of T! Directly related!
  • Units J/mol
  • KE per molecule ½ mv2 ? this is the only
    equation given on AP exam!
  • - Units J

Large! For H2 at 20C 2,000m/s
48
Root Mean Square Velocity Example
  • What is the root mean square velocity for the
    atoms in a sample of He gas at 25C?
  • Convert T to K 25 273 298K
  • M 4.00g/mol ? 0.004000kg/mol
  • urms 136m/s

49
Range of velocities
  • The average distance a molecule travels between
    collisions with another gas particle is called
    the mean free path and is small (near 10-7)
  • Results in a range of velocities.
  • Temperature is an average. There are molecules of
    many speeds in the average.
  • This is shown on a graph called a velocity
    distribution.

50
Maxwell-Boltzmann Distribution
Notice that with higher T, average velocities
increase and so does the velocity range.
273 K
1273 K
2273 K
number of particles
Molecular Velocity
51
AP Practice Question
  • Two balloons are at the same T and P. One
    contains 14g of nitrogen and the other contains
    20.0g of argon. Which of the following is true?
  • D of N2 gt D of Ar
  • Average speed of N2 gt average speed of Ar
    molecules
  • Average KE of N2 molecules gt average KE of Ar
    molecules
  • V of N2 container lt V Ar

52
AP Practice Question
  • Increasing the T of an ideal gas from 50C to
    75C at constant V will cause which of the
    following to increase for the gas?
  • average molecular mass of the gas
  • average distance between molecules
  • average speed of the molecules
  • density of the gas

53
Section 6 Homework
  • Pg. 222-223 78, 79, 82, 83

54
EFFUSION AND DIFFUSION
  • Section 5.7

55
Effusion
  • Passage of gas through a small hole, into a
    vacuum.
  • Effusion rate speed at which the gas is
    transferred into the vacuum.
  • Grahams Law - the relative rates of effusion are
    inversely proportional to the square roots of the
    molar masses of the gas particles.

56
Diffusion
  • The spreading of a gas through a room (mixing of
    gases).
  • Slow considering molecules move at hundreds of
    meters per second.
  • Slower movement is caused by collisions with
    other molecules in the air.
  • Best estimate is Grahams Law.
  • Ratio is actually less.
  • More complex analysis required.

57
Section 7 Homework
  • Pg. 223 86, 88

58
REAL GASES
  • Sections 5.8 5.9

59
Real Gases
  • Real molecules do take up space and they do
    interact with each other (especially polar
    molecules).
  • Need to add correction factors to the ideal gas
    law to account for these.
  • a correction factor for pressure
  • b correction factor for volume

60
Volume Correction
  • The actual volume free to move in is less because
    particles do take up some of the volume.
  • More molecules will have more effect (taking up
    more space).
  • Corrected volume V V - nb
  • b is a constant that differs for each gas.
  • P nRT (V-nb)

61
Pressure Correction
  • Molecules are attracted to each other- pressure
    on the container will be less than ideal gases.
  • Size of correction factor depends on the of
    molecules per liter (conc. of gas).
  • More molecules closer together and more likely
    to interact/attract.
  • Since two molecules interact, the effect must be
    squared.

(
)
2
a proportionality constant
Pobserved
P - a
62
All Together
(
)
  • Pobs nRT - a n 2 V-nb
    V
  • Called the Van der Waals equation if
    rearranged
  • Corrected Corrected Pressure
    Volume

NOT given on AP Equation sheet!
63
Graphing Real Gases
  • For ideal gases PV/nRT should be 1 (since both
    are equal according to ideal gas law).
  • Not seen for real gases.
  • Notice the effect of T on ideal gas behavior.

64
Graphing Real Gases
  • Deviation from ideal behavior depends on identity
    of the gas too.
  • Smaller, nonpolar gases exhibit more ideal
    behavior.

65
Where Do Constants Come From?
  • a and b are experimentally determined.
  • Different for each gas.
  • Bigger molecules have larger b.
  • a depends on both size and polarity.
  • Note table of constants for some gases is on pg.
    210 in the book.

66
Graphing Real Gases
  • Take a closer look at H2 on the graph.
  • Most ideal behavior, so it has lowest a value
    of the gases shown for Van der Waals equation.
  • Lower a means less correction needed.
  • Thus it must have weak intermolecular forces.
  • Real gas behavior can tell us how big of a role
    intermolecular forces play in attraction between
    gas molecules.

67
AP Practice Question
  • The true volume of a real gas is smaller than
    that calculated from the ideal gas equation. This
    occurs because the ideal gas equation does not
    consider which of the following?
  • Attraction between molecules
  • Shapes of molecules
  • Volume of molecules
  • Mass of molecules

68
AP Practice Question
  • Which of the following gases probably shows the
    greatest deviation from ideal gas behavior?
  • He
  • O2
  • SF4
  • SiH4

69
Sections 89 Homework
  • Pg. 223 89, 90
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